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<div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">#!/usr/bin/python</span>
<a name="l00002"></a>00002 <span class="comment"># -*- coding: utf-8 -*-</span>
<a name="l00003"></a>00003 
<a name="l00004"></a>00004 <span class="comment"># Copyright (c) 2011</span>
<a name="l00005"></a>00005 <span class="comment">#</span>
<a name="l00006"></a>00006 <span class="comment"># Permission is hereby granted, free of charge, to any person obtaining a</span>
<a name="l00007"></a>00007 <span class="comment"># copy of this software and associated documentation files (the &quot;Software&quot;),</span>
<a name="l00008"></a>00008 <span class="comment"># to deal in the Software without restriction, including without limitation</span>
<a name="l00009"></a>00009 <span class="comment"># the rights to use, copy, modify, merge, publish, distribute, sublicense,</span>
<a name="l00010"></a>00010 <span class="comment"># and/or sell copies of the Software, and to permit persons to whom the</span>
<a name="l00011"></a>00011 <span class="comment"># Software is furnished to do so, subject to the following conditions:</span>
<a name="l00012"></a>00012 <span class="comment">#</span>
<a name="l00013"></a>00013 <span class="comment"># The above copyright notice and this permission notice shall be included in</span>
<a name="l00014"></a>00014 <span class="comment"># all copies or substantial portions of the Software.</span>
<a name="l00015"></a>00015 <span class="comment">#</span>
<a name="l00016"></a>00016 <span class="comment"># THE SOFTWARE IS PROVIDED &quot;AS IS&quot;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR</span>
<a name="l00017"></a>00017 <span class="comment"># IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,</span>
<a name="l00018"></a>00018 <span class="comment"># FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE</span>
<a name="l00019"></a>00019 <span class="comment"># AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER</span>
<a name="l00020"></a>00020 <span class="comment"># LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,</span>
<a name="l00021"></a>00021 <span class="comment"># OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE</span>
<a name="l00022"></a>00022 <span class="comment"># SOFTWARE.</span>
<a name="l00023"></a>00023 <span class="comment">#</span>
<a name="l00024"></a>00024 <span class="comment"># Author: Jesus Carrero &lt;j.o.carrero@gmail.com&gt;</span>
<a name="l00025"></a>00025 <span class="comment"># Mountain View, CA</span>
<a name="l00026"></a>00026 
<a name="l00027"></a>00027 <span class="stringliteral">&quot;&quot;&quot; calibrate volatility curve using splines. &quot;&quot;&quot;</span>
<a name="l00028"></a>00028 
<a name="l00029"></a>00029 <span class="keyword">from</span> scipy <span class="keyword">import</span> c_, zeros, arange, linspace
<a name="l00030"></a>00030 <span class="keyword">from</span> numpy <span class="keyword">import</span> asarray
<a name="l00031"></a>00031 <span class="keyword">from</span> utils.FemBases <span class="keyword">import</span> LagrangeP1, LagrangeP2
<a name="l00032"></a>00032 
<a name="l00033"></a>00033 <span class="keyword">from</span> models.CalibBase <span class="keyword">import</span> CalibBase
<a name="l00034"></a>00034 <span class="keyword">from</span> models.NumericalOptionGBM <span class="keyword">import</span> NumericalOptionGBM
<a name="l00035"></a>00035 <span class="keyword">from</span> solvers.EuropeanTimeStepper <span class="keyword">import</span> EuropeanTimeStepper
<a name="l00036"></a>00036 
<a name="l00037"></a>00037 <span class="keyword">import</span> logging
<a name="l00038"></a>00038 
<a name="l00039"></a>00039 
<a name="l00040"></a><a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html">00040</a> <span class="keyword">class </span><a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html">CalibVolCurve</a>(<a class="code" href="classmodels_1_1CalibBase_1_1CalibBase.html">CalibBase</a>):
<a name="l00041"></a>00041     <span class="stringliteral">&quot;&quot;&quot; calibrate volatility using splines.</span>
<a name="l00042"></a>00042 <span class="stringliteral">        Adaptive stepper using a PID controller, based on::</span>
<a name="l00043"></a>00043 <span class="stringliteral"></span>
<a name="l00044"></a>00044 <span class="stringliteral">        @article{PIDpaper,</span>
<a name="l00045"></a>00045 <span class="stringliteral">            author =  {A. M. P. Valli and G. F. Carey and A. L. G. A. Coutinho},</span>
<a name="l00046"></a>00046 <span class="stringliteral">            title =   {Control strategies for timestep selection in finite element</span>
<a name="l00047"></a>00047 <span class="stringliteral">                       simulation of incompressible flows and coupled</span>
<a name="l00048"></a>00048 <span class="stringliteral">                       reaction-convection-diffusion processes},</span>
<a name="l00049"></a>00049 <span class="stringliteral">            journal = {Int. J. Numer. Meth. Fluids},</span>
<a name="l00050"></a>00050 <span class="stringliteral">                       volume =  47,</span>
<a name="l00051"></a>00051 <span class="stringliteral">                       year =    2005,</span>
<a name="l00052"></a>00052 <span class="stringliteral">                       pages =   {201-231},</span>
<a name="l00053"></a>00053 <span class="stringliteral">        }</span>
<a name="l00054"></a>00054 <span class="stringliteral">    &quot;&quot;&quot;</span>
<a name="l00055"></a>00055 
<a name="l00056"></a>00056     __slots__ = [<span class="stringliteral">&#39;m_log_progress&#39;</span>, <span class="stringliteral">&#39;m_lagrange1&#39;</span>, <span class="stringliteral">&#39;m_lagrange2&#39;</span>,
<a name="l00057"></a>00057                  <span class="stringliteral">&#39;m_market_val&#39;</span>]
<a name="l00058"></a>00058 
<a name="l00059"></a><a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a8ed4e4cbabd0a3641f11c5959863462c">00059</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a8ed4e4cbabd0a3641f11c5959863462c">__init__</a>(self):
<a name="l00060"></a>00060         <span class="stringliteral">&quot;&quot;&quot; instantiate an object of type CalibVolCurve. &quot;&quot;&quot;</span>
<a name="l00061"></a>00061         CalibBase.__init__(self)
<a name="l00062"></a>00062 
<a name="l00063"></a>00063         (self.m_tmin, self.m_tmax, self.m_min_price,
<a name="l00064"></a>00064          self.m_max_price) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>, <span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00065"></a>00065 
<a name="l00066"></a>00066         (self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#ae676adf0432ab1e10509e4c0828910a2">m_indx</a>, self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#abab24256fe7a7d080c00775cbfdb590b">m_time_spacing</a>, self.m_nt_intervals) = \
<a name="l00067"></a>00067             (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00068"></a>00068 
<a name="l00069"></a>00069         self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#adea58be65279a68e6c4718de3db2c4ff">m_lagrange1</a> = <a class="code" href="classutils_1_1FemBases_1_1LagrangeP1.html">LagrangeP1</a>()
<a name="l00070"></a>00070         self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a9a35aa489ddf6f4f79fa578d4ccb9ae1">m_lagrange2</a> = LagrangeP2()
<a name="l00071"></a>00071 
<a name="l00072"></a>00072         self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a5939e4e35510dcb8b35179b979b4b0d5">m_market_val</a> = <span class="keywordtype">None</span>
<a name="l00073"></a>00073         self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a878fb516b9f22bcaa9c7f2b615a2c72d">m_ntime_steps</a> = <span class="keywordtype">None</span>
<a name="l00074"></a>00074 
<a name="l00075"></a>00075         self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a769720242333e79623397ff35e801174">log_progress</a> = logging.getLogger(<span class="stringliteral">&#39;CalibVolCurve&#39;</span>)
<a name="l00076"></a>00076 
<a name="l00077"></a><a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a411a46af43861f780e7ef9e38cc6ed0d">00077</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a411a46af43861f780e7ef9e38cc6ed0d">get_price_range</a>(self):
<a name="l00078"></a>00078         <span class="stringliteral">&quot;&quot;&quot; get prince range. &quot;&quot;&quot;</span>
<a name="l00079"></a>00079 
<a name="l00080"></a>00080         <span class="keywordflow">return</span> (self.m_min_price, self.m_max_price)
<a name="l00081"></a>00081 
<a name="l00082"></a><a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a1f81ab18e9b85903f4ae6441e1384693">00082</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a1f81ab18e9b85903f4ae6441e1384693">set_grid_spacing</a>(self, nt_intervals, ntime_steps):
<a name="l00083"></a>00083         <span class="stringliteral">&quot;&quot;&quot; grid as used for calibration engine. &quot;&quot;&quot;</span>
<a name="l00084"></a>00084 
<a name="l00085"></a>00085         (self.m_nt_intervals, self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a878fb516b9f22bcaa9c7f2b615a2c72d">m_ntime_steps</a>) = (nt_intervals,
<a name="l00086"></a>00086                 ntime_steps)
<a name="l00087"></a>00087 
<a name="l00088"></a><a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a8b0a103dada82a4a1a53972dca6d501a">00088</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a8b0a103dada82a4a1a53972dca6d501a">set_market_value</a>(self, opt_prices):
<a name="l00089"></a>00089         <span class="stringliteral">&quot;&quot;&quot; observe option prices &quot;&quot;&quot;</span>
<a name="l00090"></a>00090 
<a name="l00091"></a>00091         self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a5939e4e35510dcb8b35179b979b4b0d5">m_market_val</a> = opt_prices
<a name="l00092"></a>00092 
<a name="l00093"></a>00093     <span class="keyword">def </span>__price_single_option(self, desp, sigma):
<a name="l00094"></a>00094         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00095"></a>00095 <span class="stringliteral">            Strike, Price, Time, Style[A, E], Contract[P, C]</span>
<a name="l00096"></a>00096 <span class="stringliteral">            Unfortunally you have to assemble the matrix from scratch (:</span>
<a name="l00097"></a>00097 <span class="stringliteral">            Parallel computing is the solution</span>
<a name="l00098"></a>00098 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00099"></a>00099 
<a name="l00100"></a>00100         (strike, price, interest_rate, time2_exp, style, cont_type) = desp
<a name="l00101"></a>00101 
<a name="l00102"></a>00102         price_engine = <a class="code" href="classmodels_1_1NumericalOptionGBM_1_1NumericalOptionGBM.html">NumericalOptionGBM</a>(style, time2_exp, price, strike,
<a name="l00103"></a>00103                             self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a878fb516b9f22bcaa9c7f2b615a2c72d">m_ntime_steps</a>, self.m_nt_intervals,
<a name="l00104"></a>00104                             self.m_min_price, self.m_max_price)
<a name="l00105"></a>00105         price_engine.set_option_cos(float(sigma), 0, interest_rate, <span class="keyword">True</span>,
<a name="l00106"></a>00106                 <span class="keyword">True</span>, <span class="keyword">True</span>)
<a name="l00107"></a>00107         price_engine.set_price_mode(<span class="stringliteral">&#39;price&#39;</span>)
<a name="l00108"></a>00108         price_engine.set_shape_functions(self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a9a35aa489ddf6f4f79fa578d4ccb9ae1">m_lagrange2</a>)
<a name="l00109"></a>00109 
<a name="l00110"></a>00110         time_stepper = <a class="code" href="classsolvers_1_1EuropeanTimeStepper_1_1EuropeanTimeStepper.html">EuropeanTimeStepper</a>()
<a name="l00111"></a>00111         time_stepper.set_dolog(<span class="keyword">False</span>)
<a name="l00112"></a>00112         time_stepper.set_number_steps(self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a878fb516b9f22bcaa9c7f2b615a2c72d">m_ntime_steps</a>)
<a name="l00113"></a>00113         time_stepper.set_time2simulate(time2_exp)
<a name="l00114"></a>00114         price_engine.set_time_stepper(time_stepper)
<a name="l00115"></a>00115 
<a name="l00116"></a>00116         <span class="keywordflow">if</span> cont_type == <span class="stringliteral">&#39;C&#39;</span>:
<a name="l00117"></a>00117             <span class="keywordflow">return</span> price_engine.price_call()
<a name="l00118"></a>00118         <span class="keywordflow">else</span>:
<a name="l00119"></a>00119             <span class="keywordflow">return</span> price_engine.price_put()
<a name="l00120"></a>00120 
<a name="l00121"></a>00121     <span class="keyword">def </span>__price_options(self, sig):
<a name="l00122"></a>00122         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00123"></a>00123 <span class="stringliteral">            This is where the power of computation is needed.</span>
<a name="l00124"></a>00124 <span class="stringliteral">            I structured the code in order to ditribute this function.</span>
<a name="l00125"></a>00125 <span class="stringliteral">            MPI, cuda, threding, whatever you want.</span>
<a name="l00126"></a>00126 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00127"></a>00127 
<a name="l00128"></a>00128         contract_id = self.get_cal_data()
<a name="l00129"></a>00129 
<a name="l00130"></a>00130         time2_mat = self.get_times2_maturity()
<a name="l00131"></a>00131         time_spacing = self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#abab24256fe7a7d080c00775cbfdb590b">m_time_spacing</a>
<a name="l00132"></a>00132         time_interval = c_[time_spacing[:-1], time_spacing[1:]]
<a name="l00133"></a>00133         model_value = zeros(self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a5939e4e35510dcb8b35179b979b4b0d5">m_market_val</a>.shape)
<a name="l00134"></a>00134 
<a name="l00135"></a>00135         <span class="keywordflow">for</span> t_interval <span class="keywordflow">in</span> time_interval:
<a name="l00136"></a>00136             cont_posi = self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#ae676adf0432ab1e10509e4c0828910a2">m_indx</a>[(t_interval[0] &lt;= time2_mat)
<a name="l00137"></a>00137                                     * (time2_mat &lt; t_interval[1])]
<a name="l00138"></a>00138             <span class="keywordflow">if</span> len(cont_posi):
<a name="l00139"></a>00139                 <span class="keywordflow">for</span> posi <span class="keywordflow">in</span> cont_posi:
<a name="l00140"></a>00140                     model_value[posi] = \
<a name="l00141"></a>00141                         self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a97c3cdc572b051b04da12e11cc04d1e3">__price_single_option</a>(contract_id[posi],
<a name="l00142"></a>00142                             sig)
<a name="l00143"></a>00143         <span class="keywordflow">return</span> model_value
<a name="l00144"></a>00144 
<a name="l00145"></a>00145     <span class="keyword">def </span>_cost_function(self, sig):
<a name="l00146"></a>00146         <span class="stringliteral">&quot;&quot;&quot; user define cost function. &quot;&quot;&quot;</span>
<a name="l00147"></a>00147 
<a name="l00148"></a>00148         <span class="keywordflow">if</span> sig &lt; 0:
<a name="l00149"></a>00149             <span class="keywordflow">return</span> -10000 * sig
<a name="l00150"></a>00150 
<a name="l00151"></a>00151         model_value = self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a77b015764608e93985575acd4181f379">__price_options</a>(sig)
<a name="l00152"></a>00152         <span class="keywordflow">return</span> sum((self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a5939e4e35510dcb8b35179b979b4b0d5">m_market_val</a> - model_value) ** 2)
<a name="l00153"></a>00153 
<a name="l00154"></a><a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a88db3b2fa23a03999527b6325be4ea85">00154</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#a88db3b2fa23a03999527b6325be4ea85">calibrate</a>(self):
<a name="l00155"></a>00155         <span class="stringliteral">&quot;&quot;&quot; calibrate model. &quot;&quot;&quot;</span>
<a name="l00156"></a>00156 
<a name="l00157"></a>00157         time2_mat = self.get_times2_maturity()
<a name="l00158"></a>00158         (tmin, tmax) = (min(time2_mat) * 0.95, max(time2_mat) * 1.1)
<a name="l00159"></a>00159         (self.m_min_price, self.m_max_price) = (10, 130)
<a name="l00160"></a>00160 
<a name="l00161"></a>00161         self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#abab24256fe7a7d080c00775cbfdb590b">m_time_spacing</a> = asarray(linspace(tmin, tmax, 10, <span class="stringliteral">&#39;False&#39;</span>))
<a name="l00162"></a>00162         self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#ae676adf0432ab1e10509e4c0828910a2">m_indx</a> = arange(0, self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#abab24256fe7a7d080c00775cbfdb590b">m_time_spacing</a>.size + 1)
<a name="l00163"></a>00163         <span class="keywordflow">return</span> (self.<a class="code" href="classmodels_1_1CalibVolCurve_1_1CalibVolCurve.html#abab24256fe7a7d080c00775cbfdb590b">m_time_spacing</a>, self._calibrate())
<a name="l00164"></a>00164 
<a name="l00165"></a>00165 
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